Origins versus fingerprints of the Jahn-Teller effect in d-electron ABX_{3} perovskites

Abstract

The Jahn-Teller distortion that can remove electronic degeneracies in partially occupied states and results in systematic atomic displacements is a common underlying feature to many of the intriguing phenomena observed in 3d perovskites, encompassing magnetism, superconductivity, orbital ordering, and colossal magnetoresistance. Although the seminal Jahn and Teller theorem was postulated almost a century ago, the origins of this effect in perovskite materials are still debated, including propositions such as superexchange, spin-phonon coupling, sterically induced lattice distortions, and strong dynamical correlation effects. Although the end result of Jahn-Teller distortions often includes a mix of such various contributions, due to coupling of various lattice, spin, and electronic modes with the distortions (“fingerprints” or “consequences” of Jahn-Teller), it is not clear what the primary cause is, i.e., which cases are caused by a pure electronic instability associated with degeneracy removal, as implied in the Jahn-Teller theorem, and which cases originate from other causes, such as semiclassical size effects. We propose a way to distinguish the materials with an electronic instability associated with degeneracy removal being the primary cause of the Jahn-Teller distortions, from others with octahedral rotation or tilts from a steric effect playing the primary role in electron-lattice coupling. This work provides a unified and quantitative density functional theory explanation of the experimentally observed trends of octahedral deformations in ABX_{3} perovskites, without recourse to the dynamically correlated vision of electron interactions codified by the Mott-Hubbard mechanism. We inquire about the origin and predictability of different types of octahedral deformation by using a Landau-esque approach, where the orbital occupation pattern of a symmetric structure is perturbed, finding whether it is prone to total energy lowering the electronic instability or not. This is done for a systematic series of ABX_{3} perovskite compounds having 3d-orbital degeneracies, using the density functional approach. We identify (i) systems prone to an electronic instability (a true Jahn-Teller effect), such as KCrF_{3}, KCuF_{3}, LaVO_{3}, KFeF_{3}, and KCoF_{3}, where the instability is independent of magnetic order, and forces a specific orbital arrangement that is accommodated by a BX_{6} octahedral deformation with a specific symmetry. On the other hand, (ii) compounds such as LaTiO_{3} and LaMnO_{3} with delocalized d states do not show any electronically driven instability. Here, the alternate orbital ordering, which is an energy-lowering event irrespective of the presence of electronic instabilities, simply results from the coupling of lattice modes induced by semiclassical size effects (sterically induced), such as BX_{6} octahedra rotations. (iii) Although RVO_{3} (R=Lu-La, Y) perovskites exhibit hybridizations similarly to LaTiO_{3}, their t_{2g}^{2} electronic structure is highly unstable and preserves the Jahn-Teller effect. However, here coexisting steric deformations and Jahn-Teller distortions result in strongly entangled spin-orbital properties.